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In this work we put forward an effective Gaussian free field description ofcritical wavefunctions at the transition between plateaus of the integerquantum Hall effect. To this end, we expound our earlier proposal that powersof critical wave intensities prepared via point contacts behave as pure scalingfields obeying an Abelian operator product expansion. Our arguments employ theframework of conformal field theory and, in particular, lead to amultifractality spectrum which is parabolic. We also derive a number of old andnew identities that hold exactly at the lattice level and hinge on thecorrespondence between the Chalker-Coddington network model and asupersymmetric vertex model.

Gaussian free fields at the integer quantum Hall plateau transition